A079379 -id:A079379 - cp's OEIS frontend

A079378 Costé prime expansion of (sqrt(5)-1)/2.

2, 5, 7, 5, 5, 2, 11, 5, 2, 13, 11, 5, 5, 5, 5, 2, 5, 3, 5, 11, 2, 79, 37, 11, 5, 3, 7, 17, 59, 23, 11, 2, 17, 7, 3, 7, 7, 383, 337, 67, 13, 19, 47, 23, 41, 17, 17, 13, 67, 71, 47, 17, 11, 19, 73, 53, 17, 13, 37, 19, 11, 5, 13, 29, 43, 47, 17, 5, 5, 11, 3, 3, 17, 5, 97, 29, 11, 3, 3, 3, 7

Offset: 0

N. J. A. Sloane, Feb 16 2003

For x in (0,1], define P(x) = min{p: p prime, 1/x < p}, Phi(x) = P(x)x - 1. Costé prime expansion of x(0) is sequence a(0), a(1), ... given by x(n) = Phi(x(n-1)) (n>0), a(n) = P(x(n)) (n >= 0).

G. C. Greubel, Table of n, a(n) for n = 0..2000
A. Costé, Sur un système fibré lié à la suite des nombres premiers, Exper. Math., 11 (2002), 383-405.

Cf. A079379, A079380, A079366, A079367, A079368.

Digits := 500: P := proc(x) local y; y := ceil(evalf(1/x)); if isprime(y) then y else nextprime(y); fi; end; F := proc(x) local y,i,t1; y := x; t1 := []; for i from 1 to 100 do p := P(y); t1 := [op(t1),p]; y := p*y-1; od; t1; end; F((sqrt(5)-1)/2);

$MaxExtraPrecision = 500; P[x_] := Module[{y}, y = Ceiling[1/x]; If[PrimeQ[y], y, NextPrime[y]]]; F[x_] := Module[{y, i, t1}, y = x; t1 = {}; For[i = 1, i <= 100, i++, AppendTo[t1, p = P[y]]; y = p*y - 1]; t1]; F[(Sqrt[5] -1)/2] (* G. C. Greubel, Jan 20 2019 *)

More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 17 2003

A079380 Where records occur in A079378.

Original entry on oeis.org

1, 2, 3, 7, 10, 22, 38, 111, 200, 1193

Offset: 1

N. J. A. Sloane, Feb 16 2003

RECORDS transform of A079378.

N. J. A. Sloane, Transforms

Cf. A079378, A079379, A079366-A079368.

A079378 = Cases[Import["https://oeis.org/A079378/b079378.txt", "Table"], {, }][[All, 2]];
a = {}; l = 0;
For[i = 1, i <= Length[A079378], i++,
  If[A079378[[i]] > l, l = A079378[[i]]; AppendTo[a, i]]];
a (* Robert Price, Mar 14 2020 *)

a(8)-a(10) from Robert Price, Mar 14 2020

cp's OEIS Frontend

A079378 Costé prime expansion of (sqrt(5)-1)/2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Extensions